Geoscience Reference
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the
average
velocity in the formation, which is simply the thickness in depth divided
by the thickness in (one-way) time. For the seismic ray travelling vertically through the
medium, the (two-way) travel-time
t
increases with depth
z
according to
d
z
d
t
=
(
v
0
+
kz
)
2
.
Therefore
t
2
z
2
d
t
2
=
d
z
(
v
0
+
kz
)
t
1
z
1
so
k
(
t
2
−
t
1
)
ln
v
kz
2
v
0
+
kz
1
+
0
=
2
and thus
e
k
(
t
2
−
t
1
)
/
2
v
+
kz
2
=
(
v
+
kz
1
)
·
.
0
0
Therefore,
(
v
0
+
kz
1
)
·
e
k
(
t
2
−
t
1
)
/
2
−
v
0
z
2
=
.
k
Whatever approach is adopted to splitting up the overburden into layers, a compli-
cation that often arises is that the depth map is distorted beneath zones where there is
sharp lateral variation in the overburden, for instance under dipping fault planes. This
However, this is not observed in practice, except for pre-stack depth migrated data; if
there is a significant velocity contrast between layer 1 and layer 2, there will be ray-
bending at the fault plane, which will affect different offsets differently, leading to a
smearing out of the expected kink in the stacked and migrated data. The quality of the
reflected event will deteriorate under the fault plane, and the interpreter may have to
pick through the noisy data by extrapolating the dip of the reflector as seen away from
Layer 1
Black: d
epth structure
Red: base layer 2
on time section
Fig. 3.25
Sketch of distortion of layer geometry on time section caused by a fault.
